Distributions from which the transition kernels of the
MCMC are defined, as explained hereafter. In the
following of this paragraph, means that the
realization is obtained according to the
Distribution of the list proposal of size . The underlying
MCMC algorithm is a Metropolis-Hastings one which draws candidates (for the
next state of the chain) using a random walk: from the current state
, the candidate for
can be expressed as
where the
distribution of does not depend on
. More precisely, here, during the
Metropolis-Hastings iteration, only the component
of , with , is
not zero and where
is a deterministic scalar calibration coefficient and
where . Moreover, by default,
but adaptive strategy based on the acceptance rate of each component can be
defined using the method setCalibrationStrategyPerComponent().

Notes

A RandomWalkMetropolisHastings enables to carry out MCMC
sampling according to the preceding statements. It is important to note that
sampling one new realization comes to carrying out Metropolis-
Hastings iterations (such as described above): all of the components of the new
realization can differ from the corresponding components of the previous
realization. Besides, the burn-in and thinning parameters do not take into
consideration the number of MCMC iterations indeed, but the number of sampled
realizations.

Sequence whose the component corresponds to the acceptance
rate of the candidates obtained from a state
by only changing its component, that
is to the acceptance rate only relative to the MCMC
iterations such that (see the paragraph dedicated to the
constructors of the class above). These are global acceptance rates over
all the MCMC iterations performed.

A list of CalibrationStrategy strategy, whose component
defines whether and how the (see the
paragraph dedicated to the constructors of the class above) are rescaled,
on the basis of the last component acceptance rate
. The calibration coefficients are rescaled every
MCMC iterations with
, thus on the basis of the
acceptances or refusals of the last candidates obtained by only
changing the component of the current state:
where
is defined by .

The indices of the components that are not tuned, and sampled according to
the prior distribution in order to take into account the intrinsic
uncertainty, as opposed to the epistemic uncertainty corresponding to the
tuned variables.

Sequence of values randomly determined from the RandomVector definition.
In the case of an event: one realization of the event (considered as a
Bernoulli variable) which is a boolean value (1 for the realization of the
event and 0 else).

n sequences of values randomly determined from the RandomVector definition.
In the case of an event: n realizations of the event (considered as a
Bernoulli variable) which are boolean values (1 for the realization of the
event and 0 else).

A list of CalibrationStrategy strategy, whose component
defines whether and how the (see the
paragraph dedicated to the constructors of the class above) are rescaled,
on the basis of the last component acceptance rate
. The calibration coefficients are rescaled every
MCMC iterations with
, thus on the basis of the
acceptances or refusals of the last candidates obtained by only
changing the component of the current state:
where
is defined by .

The indices of the components that are not tuned, and sampled according to
the prior distribution in order to take into account the intrinsic
uncertainty, as opposed to the epistemic uncertainty corresponding to the
tuned variables.